Nonlinear estimation of the BOLD signal

Signal variations in functional Magnetic Resonance Imaging experiments essentially reflect the vascular system response to increased demand for oxygen caused by neuronal activity, termed the blood oxygenation level dependent (BOLD) effect. The most comprehensive model to date of the BOLD signal is formulated as a mixed continuous-discrete-time system of nonlinear stochastic differential equations. Previous approaches to the analysis of this system have been based on linearised approximations of the dynamics, which are limited in their ability to capture the inherent nonlinearities in the physiological system. In this paper we present a nonlinear filtering method for simultaneous estimation of the hidden physiological states and the system parameters, based on an iterative coordinate descent framework. State estimates of the cerebral blood flow, cerebral blood volume and deoxyhaemoglobin content are determined using a particle filter, demonstrated via simulation to be accurate, robust and efficient in comparison to linearisation-based techniques. The adaptive state and parameter estimation algorithm generates physiologically reasonable parameter estimates for experimental fMRI data. It is anticipated that signal processing techniques for modelling and estimation will become increasingly important in fMRI analyses as limitations of linear and linearised modelling are reached.